Evaluation of LS-DYNA Concrete Material Model 159

508 Compliance Captions

Figure 1. Graph. The default behavior of the concrete model in uniaxial tensile stress and pure shear stress is linear to the peak, followed by brittle softening. The vertical axis of this graph ranges from 0 to 2.4 and represents Stress (megapascals) while the horizontal axis of this graph ranges from 0 to 0.008 and represents Displacement (centimeters). The solid or red line depicts Tension and starts at 0 and rises to 2.2 on the vertical axis and to approximately 0.0004 on the horizontal axis, where it peaks and gradually slopes back down to 0.1 on the vertical axis and 0.008 on the horizontal axis. The dashed or blue line depicts Shear and starts at 0 and rises to 2.1 on the vertical axis and to approximately 0.0009 on the horizontal axis, where it peaks and gradually slopes back down to the 0.1 on the vertical axis and 0.008 on the horizontal axis, where both lines leave the graph.

Figure 2. Graph. Strength and ductility increase with confining pressure in these triaxial compression simulations. The vertical axis of this graph depicts Stress (megapascals) and ranges from negative 42 to negative 1. The horizontal axis represents Displacement (centimeters) and ranges from 0 to 0.026. The graph shows three lines starting at negative 1 on the vertical axis and 0 on the horizontal axis. The red or solid line (representing 0 megapascals confinement) falls to negative 28 on the verical axis and 0.0045 on the horizontal axis and then climbs through negative 11 on the vertical axis and 0.0145 on the horizontal axis and ends at negative 1.5 on the vertical axis and 0.0245 on the horizontal axis. The blue or long-dashed line (representing 1.4 megapascals confinement) falls along the same trajectory, then at negative 35 on the vertical axis and 0.005 on the horizontal axis starts curving through negative 26 on the vertical axis and 0.012 on the horizontal axis, peaking and leaving the graph at negative 14 on the vertical axis. The green or short-dashed line (representing 2.8 megapascals confinement) falls along the same trajectory, stopping at negative 40 on the vertical axis and 0.006 on the horizontal axis and curving through negative 31 on the vertical axis and 0.012 on the horizontal and peaking at negative 20 on the vertical axis, where it leaves the graph.

Figure 3. Graph. The concrete model simulates volume expansion in uniaxial compressive stress, in agreement with typical test data (strains and stress positive in compression). The vertical axis of this graph depicts Stress (megapascals) and ranges from 0 to 40. The horizontal axis represents Strain and ranges from negative 0.002 to 0.002. The graph shows three lines. The black or solid line (Axial) starts at at 0 on the vertical axis and 0 on the horizontal axis. It rises on a straight trajectory to 35 on the vertical axis and 0.00125 on the horizontal axis then it starts to fall leaving the graph at 31.5 on the vertical axis. The blue or long-dashed line (Lateral) starts at 31.5 on the vertical axis and negative 0.002 on the horizontal axis and gradually rises to 35 on the vertical axis and nearly 0 on the horizontal axis, and falls on a straight trajectory to 0 on the vertical axis and 0 on the horizontal axis. The red or short-dashed line (Volumetric) starts at 31.5 on the vertical axis and negative 0.002 on the horizontal axis and gradually rises to 35 on the vertical axis and negative 0.001 on the horizontal axis, where it slopes on a straight trajectory to 0 on the vertical axis and 0 on the horizontal axis.

Figure 4. Graph. The modulus of concrete degrades with strength, as demonstrated by this cyclic loading simulation. The vertical axis of this graph depicts Stress (megapascals) and ranges from negative 3.5 to 3.5. The horizontal axis represents Strain and ranges from 0 to 0.0022. The line starts at 0 on the vertical axis and 0 on the horizontal axis it rises to 3 on the vertical axis and 0.0001 on the horizontal line. This point is labeled "Undamaged Modulus." The line curves downward as the modulus degrades to 1 on the vertical axis and 0.0009 on the horizontal axis. The line falls through 0 on the vertical axis and 0.0008 on the horizontal axis to negative 3.5 on the vertical axis and 0.0007 on the horizontal axis before recovering to 1 on the vertical axis and 0.0009 on the horizontal axis and continuing to curve, ending at 0.25 on the vertical axis and 0.0021 on the horizontal axis.

Figure 5. Graph. The difference in pressure at a given volumetric strain for these isotropic compression and uniaxial strain simulations is due to shear enhanced compaction. The vertical axis of this graph depicts Pressure (megapascals) and ranges from 0 to 160. The horizontal axis represents Volumetric Strain and ranges from 0 to 0.02. There are two lines depicted on this graph, both starting at 0 on the vertical axis and 0 on the horizontal axis. The solid or black line (Isotropic Compression) rises to 30 on the vertical axis and 0.0025 on the horizontal axis and then rises in a straight trajectory leaving the graph at 160 on the vertical axis and 0.02 on the horizontal axis. The dashed or red line (Uniaxial Strain) rises to 25 on the vertical axis and 0.0025 on the horizontal axis and then changes direction and rises on a straight trajectory, leaving the graph at 141 on the vertical axis and 0.02 on the horizontal axis.

Figure 6. Graph. The increase in strength with strain rate is significant in tension at a strain rate of 100 per second. The vertical axis of this graph depicts Stress (megapascals) and ranges from 0 to 13. The horizontal axis represents Displacement (millimeters) and ranges from 0 to 0.2. The graph has three lines. The solid or black line (Quasi-static) rises from 0 on the vertical axis and 0 on the horizontal axis to 2 on the vertical axis and 0.0025 on the horizontal axis, then curves down and meets and goes along the vertical axis at 0 at 0.1 on the horizontal axis. The long-dashed or red line (100 per second with repow equal to 0) rises from 0 on the vertical axis and 0 on the horizontal axis to a peak of 12.5 on the vertical axis and 0.03 on the horizontal axis before falling to 0 on the vertical axis and meeting and following the horizontal axis at 0.04. The short-dashed red line (100 per second with repow equal to 1) starts in the graph at 12.5 on the vertical axis and 0.03 on the horizontal axis or at the peak of the long-dashed line and falls steeply through 1.5 on the vertical axis and 0.1 on the horizontal to meet the vertical axis at 0 at 0.18 on the horizontal axis.

Figure 7. Graph. The increase in strength with strain rate in pure shear stress is similar to that modeled in uniaxial tensile stress. The vertical axis of this graph depicts Stress (megapascals) and ranges from 0 to 13. The horizontal axis represents Displacement (millimeters) and ranges from 0 to 0.2. The graph has three lines similar to figure 6. The solid or black line (Quasi-static) rises from 0 on the vertical axis and 0 on the horizontal axis to 2 on the vertical axis and 0.0025 on the horizontal axis and then curves downward and meets and goes along the vertical axis at 0 at 0.1 on the horizontal axis. The long-dashed or red line (100 per second with repow equal to 0) rises from 0 on the vertical axis and 0 on the horizontal axis to a peak of 13 on the vertical axis and 0.045 on the horizontal axis before falling to 0 on the vertical axis and meeting and following the horizontal axis at 0.08. The short-dashed red line (100 per second with repow equal to 1) starts in the graph at 13 on the vertical axis and 0.045 on the horizontal axis or at the peak of the long-dashed line and falls steeply through 3 on the vertical axis and 0.12 on the horizontal and leaves the graph at 1 on the vertical axis and 0.2 on the horizontal axis.

Figure 8. Graph. The increase in strength with strain rate in uniaxial compression stress is less pronounced than in uniaxial tensile stress or pure shear stress. This graph has the same three lines as Figures 6 and 7. The vertical axis of this graph depicts Stress (megapascals) and ranges from negative 50 to 0. The horizontal axis represents Displacement (millimeters) and ranges from 0 to 0.6. The solid or black line (Quasi-static) starts at 0 on the vertical axis and 0 on the horizontal axis and falls to negative 28 on the vertical axis and 0.04 on the horizontal axis and then curves upward and goes through negative 5 on the vertical axis and 0.35 on the horizontal axis and leaves the graph at negative 1 on the vertical axis and 0.6 on the horizontal axis. The long-dashed or red line (100 per second with repow equal to 0) falls from 0 on the vertical axis and 0 on the horizontal axis to a low of negative 47 on the vertical axis and 0.06 on the horizontal axis before rising to negative 12 on the vertical axis and 0.35 on the horizontal axis and leaving the graph at negative 8 on the vertical axis and 0.6 on the horizontal axis. The short-dashed red line (100 per second with repow equal to 1) starts in the graph at negative 47 on the vertical axis and 0.06 on the horizontal axis, or at the low point of the long-dashed line, and rises through negative 15 on the vertical axis and 0.35 on the horizontal axis, leaving the graph at negative 8.5 on the vertical axis and 0.6 on the horizontal axis.

Figure 9. Graph. Application of kinematic hardening simulates prepeak nonlinearity accompanied by plastic volume expansion. The vertical axis of this graph depicts Stress (megapascals) and ranges from negative 30 to 0. The horizontal axis represents Strain and ranges from 0 to 0.016. The graph has two lines. The solid or red line (Without Kinematic Hardening) falls from 0 on the vertical axis and 0 on the horizontal axis to a low point of negative 28 on the vertical axis and 0.0015 on the horizontal axis, then curves up through negative 2 on the vertical axis and 0.012 on the horizontal axis, and leaves the graph at negative 0.5 on the vertical axis and 0.016 on the horizontal axis. The dashed or blue line (With Kinematic Hardening) falls from 0 on the vertical axis and 0 on the horizontal axis to a low point of negative 28 on the vertical axis and 0.0025 on the horizontal axis before rising and going through negative 3 on the vertical axis and 0.01 on the horizontal axis and leaving the graph at negative 0.5 on the vertical axis and 0.016 on the horizontal axis.

Figure 13. Illustration. The damage mode calculated for compression cylinders with fixed ends agrees with the X-shaped damage bands observed in tests. This figure shows the damage simulation in one concrete cylinder at different times and orientations. The first three views are at the end of the calculation at 1.5 seconds. In one view, the cylinder is sliced in half vertically to reveal two diagonal bands of damage on the vertical midplane. In the next view, the cylinder is whole and the two diagonal bands are revealed on the outside of the cylinder. In the third view, the cylinder is rotated on its axis ninety degrees, such that the damage looks like an "O." The next three views show how the damage accumulates with time, for a cylinder sliced in half vertically. At 0.5 second, the damage is concentrated at the center of the cylinder. By 0.65 second, two weak diagonal bands of damage form a weak "X." By 1.0 second, two strong diagonal bands are evident.

Figure 15. Illustration. A diagonal band of damage is calculated with frictional end constraints if both end caps are allowed to rotate and slide (no end cap constraints). This figure shows the damage simulated in one concrete cylinder at three different times, and two views. In the first three views, the cylinder is sliced in half vertically to reveal the cylinder midplane. By 400 milliseconds, a weak diagonal band of damage has formed, and spreads from the top right side, about three-fourths of the way down to the left side. By 1 second, the damage band has grown stronger and wider. By 3 seconds, the diagonal spreads across seven elements. The midplane cylinder mesh is 16 elements high and 8 elements wide. A view of the outside of the cylinder at 3 seconds reveals that one element has eroded.

Figure 16. Illustration. A diagonal band of damage is calculated with frictional end constraints if one end cap is allowed to rotate or slide relative to the other (bottom cap constrained from rotating and sliding). This figure shows the damage simulated in one concrete cylinder at three different times, and two views. The damage is quite similar to that previously discussed in Figure 14. In the first three views, the cylinder is sliced in half vertically to reveal the cylinder midplane. By 400 milliseconds, a weak diagonal band of damage has formed, and spreads from the top right side, about three-fourths of the way down to the left side. By 1 second, the damage band has grown stronger and wider. By 3 seconds, the diagonal spreads across seven elements. The midplane cylinder mesh is 16 elements high and 8 elements wide. A view of the outside of the cylinder at 3 seconds reveals that two elements have eroded.

Figure 17. Illustration. A double diagonal band of damage is initially calculated if both end caps are prevented from rotating and sliding (bottom and top caps constrained from rotating and sliding). This figure shows the damage simulated in one concrete cylinder at three different times, and two views. In the first three views, the cylinder is sliced in half vertically to reveal the cylinder midplane. By 400 milliseconds, a weak concentration of damage is simulated at the center of the cylinder. By 1 second, the damage has grown into two diagonal bands, initiating at the top of the cylinder, and extending about three-fourths of the way down. By 3 seconds, the diagonal grows stronger, and the cylinder bulges. The midplane cylinder mesh is 16 elements high and 8 elements wide. A view of the outside of the cylinder at 3 seconds reveals the buldges.

Figure 18. Illustration. A double diagonal band of damage is initially calculated if one end cap is free to rotate (bottom cap restrained from rotating and sliding, top cap restrained from sliding). This figure shows the damage simulated in one concrete cylinder at three different times, and two views. Damage is similar to that previously shown in Figure 17, for a cylinder with bottom and top caps that are constrained from rotating and sliding. In the first three views, the cylinder is sliced in half vertically to reveal the cylinder midplane. By 400 milliseconds, a weak concentration of damage is simulated at the center of the cylinder. By 1 second, the damage has grown into two diagonal bands, initiating at the top of the cylinder, and extending about three-fourths of the way down. By 3 seconds, the diagonal grows stronger, and the cylinder bulges. The midplane cylinder mesh is 16 elements high and 8 elements wide. A view of the outside of the cylinder at 3 seconds reveals the buldges.

Figure 19. Illustration. A single diagonal band of damage initiates, but is not retained, if the cylinder is over-constrained (bottom and top caps restrained from sliding). This figure shows the damage simulated in one concrete cylinder at three different times, and two views. Damage is similar to that previously shown in Figures 17 and 18. In the first three views, the cylinder is sliced in half vertically to reveal the cylinder midplane. By 400 milliseconds, a weak concentration of damage is simulated at the center of the cylinder. By 1 seccond, the damage has grown into two diagonal bands, initiating at the top of the cylinder, and extending about three-fourths of the way down. By 3 seconds, the diagonal grows stronger, and the cylinder bulges. The midplane cylinder mesh is 16 elements high and 8 elements wide. A view of the outside of the cylinder at 3 seconds reveals the buldges.

Figure 21. Graph. Differences in initial slope are primarily due to differing amounts of contract surface penetration between the concrete cylinder and end caps. The vertical axis of this graph depicts Stress in megapascals and ranges from negative 48 to 0. The horizontal axis represents Time in seconds and ranges from 0 to 1.5. The graph has three lines all originating at 0 on the vertical axis and 0 on the horizontal axis. The solid or blue line (Constraint Nodes to Surface SFS equals 1) falls on a straight trajectory to a low of negative 44 on the vertical axis and 0.25 on horizontal axis rising through negative 24 on the vertical axis, and 0.65 on the horizontal axis continuing upward in a ragged curve and leaving the graph at negative 17 on the vertical axis and 1.5 on the horizontal axis. The long-dashed or red line (Automatic Surface to Surface SFS equals 1) falls from 0 on the vertical axis and 0 on the horizontal axis to a low point of negative 45 on the vertical axis and 0.45 on the horizontal axis before rising through negative 24 on the vertical axis and 0.8 on the horizontal axis and leaving the graph at negative 19 on the vertical axis and 1.5 on the horizontal axis. The short-dashed green line (Automatic Surface to Surface SFS equals 10) falls to a low of negative 43 on the vertical axis and 0.35 on the horizontal axis before rising through negative 28 on the vertical axis and 0.8 on the horizontal axis, and leaves the graph at negative 21 on the vertical axis and 1.5 on the horizontal axis.

Figure 22. Graph. End cap versus concrete dispalcement with penetration (SFS equals 1). This graph is output directly from LS-POST. The Y-axis is Axial Displacement in millimeters, and ranges from negative 4 to 1. The X-axis is Time in seconds and ranges from 0 to 1.5. This graph shows six lines. Nodes 1 and 8001 give the displacement histories at each end of the cylinder. Nodes 9001 and 9501 give the displacement histories of each steel cap at the interface with the concrete cylinder. Nodes 18001 and 18501 give the displacement histories of the cap on the top and bottom free surfaces. If no penetration exists, then the histories for all three top end nodes should be identical, and the histories for all three bottom end nodes should be identical. This is not the case. At the bottom end, the cap nodal histories are uniformly 0, whereas the concrete nodal history peaks at a compressive displacement of negative 0.35 at about 0.5 seconds. On the top end, the cap nodal histories are identical and linear from 0 0 to negative 3.8 millimeters at 1.5 seconds. The concrete nodal history is slightly nonlinear, from 0 0 to negative 3.7 millimeters at 1.5 seconds.

Figure 23. Graph. End cap versus concrete displacement with little penetration (SFS equals 10). This graph is output directly from LS-POST. The Y-axis is Axial Displacement in millimeters, and ranges from negative 4 to 1. The X-axis is Time in seconds and ranges from 0 to 1.5. This graph shows six lines. Nodes 1 and 8001 give the displacement histories at each end of the cylinder. Nodes 9001 and 9501 give the displacement histories of each steel cap at the interface with the concrete cylinder. Nodes 18001 and 18501 give the displacement histories of the cap on the top and bottom free surfaces. The histories for all three top end nodes are identical, and the histories for all three bottom end nodes are identical. On the bottom, they remain uniform at 0 displacement. On the top, the nodal histories are linear from 0 0 to negative 3.8 millimeters at 1.5 seconds.

Figure 24. Graph. The relative displacement between the ends of the concrete cylinder depends upon the amount of interface penetration present. This graph has three lines starting at 0 on the vertical axis and 0 on the horizontal axis. The vertical axis of this graph depicts Relative Displacement (millimeters) and ranges from negative 4 to 0. The horizontal axis represents Time (seconds) and ranges from 0 to 1.6. The solid or blue line (Constraint Nodes to Surface SFS equals 1) falls from 0 on the vertical axis and 0 on the horizontal axis in a straight trajectory to negative 0.4 on the vertical axis and 1.59 on the horizontal axis. The long-dashed or red line (Automatic Surface to Surface SFS equals 1) falls from 0 on the vertical axis and 0 on the horizontal axis through a curve at negative 0.5 on the vertical axis and 0.4 on the horizontal axis and then leaving the graph at negative 4 on the vertical axis and 1.6 on the horizontal axis. The short-dashed green line (Automatic Surface to Surface SFS equals 10) falls in a straight trajectory, leaving the graph at negative 4 on the vertical axis and 1.6 on the horizontal axis.

Figure 25. Graph. The stress-displacement histories are in reasonable agreement if the relative displacement of the cylinder is used. This graph has three lines starting at 0 on the vertical axis and 0 on the horizontal axis. The vertical axis of this graph depicts Stress (megapascals) and ranges from negative 48 to 0. The horizontal axis represents Displacement (millimeters) and ranges from 0 to 3.8. The solid or blue line (Constraint Nodes to Surface SFS equals 1) falls from 0 on the vertical axis and 0 on the horizontal axis in a straight trajectory to negative 44 on the vertical axis and 0.45 on the horizontal axis. It then curves upward through negative 24 on the vertical axis 1.6 on the horizontal axis, following a ragged line and leaving the graph at negative 17 on vertical line and 3.8 on the horizontal line. The long-dashed or red line (Automatic Surface to Surface SFS equals 1) falls from 0 on the vertical axis and 0 on the horizontal axis to a low point of negative 44 on the vertical axis and 0.45 on the horizontal axis, then rises following the solid line and leaving the graph at approximately negative 18 on the vertical axis. The short-dashed green line (Automatic Surface to Surface SFS equals 10) falls in a straight trajectory to a low of negative 43 and curving upward through negative 28 on the vertical axis and 1.6 on the horizontal axis negative 21 on the vertical axis and 3.8 on the horizontal axis.

Figure 27. Graph. The fracture energy, which is the area under the softening portion of the stress-displacement curve, is independent of element size in the direct pull simulations, (not shifted). The vertical axis measures Stress (megapascals) and ranges from 0 to 3.5 megapascals. The horizontal axis measure Displacement (millimeters) and ranges from 0 to 0.05 millimeters. This graph has four lines each starting at 0 on the vertical axis and 0 on the horizontal axis. Each curve increases linearly to a peak of 3.4 megapascals, then softens nonlinearly. The time at which each curves peaks depends on the element size. The time to the peak increases with increasing element: 0.002 for 12.7-millimeter element size, 0.0045 for 38.1-millimeter element size, 0.009 for 76.2-millimeter element size, and 0.017 for 152.4-millimeter element size.

Figure 29. Graph. Although the fracture energy is constant, the softening curves vary slightly with element size in the unconfined compression simulations (not shifted). The vertical axis measures Stress (megapascals) and ranges from negative 50 to 0 megapascals. The horizontal axis measures Displacement (millimeters) and ranges from 0 to 0.5 millimeter. This graph has four lines each starting at 0 on the vertical axis and 0 on the horizontal axis. Each curve decreases in a linear manner to a peak of negative 46 megapascals, then softens nonlinearly. The time at which each curves peaks depends on the element size. The time to the peak increases with increasing element size: 0.02 for 12.7-millimeter element size, 0.055 for 38.1-millimeter element size, 0.011 for 76.2-millimeter element size, and 0.023 for 152.4-millimeter element size.

Figure 32. Graph. The stress-displacement curves calculated in direct pull with an unregulated softening formulation do not converge as the mesh is refined. The Y-axis is Stress in megapascals, and ranges from 0 to 3.5 megapascals. The X-axis is Displacement in millimeters and ranges from 0 to 0.1 millimeter. Four curves are shown for four different element sizes. These are 1, 2, 768, and 2,592 elements. All four curves are linear to the peak, and identical to the peak. They originate at 0,0 and peak at 3.5 megapascals at 0.032 millimeter. Then each curve softens in a nonlinear manner. The softening becomes more brittle as the element size increases. The single element softening curve is nearly linear and ends at 3.1 megapascals at 0.1 millimeter. The double element softening curve is nearly linear and ends at 2.75 megapascals at 0.1 millimeter. The 768 elements softening curve is nonlinear and ends at 0.3 megapascals at 0.1 millimeter. The 2,592 elements softening curve is nonlinear and ends at 0.1 megapascals at 0.1 millimeter.

Figure 33. Illustration. The damage mode calculated in direct pull with an unregulated softening formulation is damage within a single band of elements. This figure shows the damage in each mesh for four refinements: one element, two elements, basic mesh, and refined mesh. For one element, the damage is uniform top to bottom. For two elements, the damage dominates the top element. For the basic mesh, the damage is a single horizontal band located just above the vertical midplane. For the refined mesh, the damage is a single horizontal band located at the bottom row of elements.

Figure 34. Graph. The stress-displacement curves calculated in unconfined compression with an unregulated softening formulation are similar for the basic and refined meshes (fixed ends). The Y-axis is Stress in megapascals, and ranges from negative 65 to 0. The X-axis is Displacement in millimeters, and ranges from 0 to 3.8. Four curves are shown for four element sizes. The single element curve is nearly linear and decreases from the origin to negative 65 megapascals at 0.7 millimeter. The other three curves are linear to a peak of 46 megapascals at 0.42 millimeter. The two elements curve softens gradually to negative 7.5 megapascals at 3.8 millimeters. The 768 elements curve softens with more brittleness at first, but then reaches a plateau of negative 21 megapascals at 3.8 millimeters. The 2,592 elements curve softens with the most brittleness at first, but then reaches a plateau of negative 19.5 megapascals at 3.8 millimeters.

Figure 35. Illustration. The damage mode calculated in unconfined compression with an unregulated softening formulation is a double diagonal (in the basic and refined meshes with fixed end conditions). This figure shows the damage in each mesh for four refinements: one element, two elements, basic mesh, and refined mesh. For one and two elements, the damage is uniform top to bottom. For two elements, a bulge is evident at the vertical midplane. For the basic and refined meshes, the damage is two diagonal bands in the form of an X located about the vertical midplane. The damage bands for the refined mesh are narrower and more distinct than those of the basic mesh.

Figure 36. Graph. The stress-displacement curves calculated in direct pull with a regulated softening formulation converge as the mesh is refined. The Y-axis is Stress in megapascals, and ranges from 0 to 3.5 megapascals. The X-axis is Displacement in millimeters and ranges from 0 to 0.1 millimeter. Four curves are shown for four different element sizes. These are 1, 2, 768, and 2,592 elements. All four curves are linear to the peak, and identical to the peak. They originate at 0,0 and peak at 3.5 megapascals at 0.032 millimeter. Then each curve softens in a nonlinear manner. The softening becomes more brittle as the element size increases, but lie on top of each other for 768 and 2,592 elements. The single element softening curve is nearly linear and ends at 0.8 megapascal at 0.1 millimeter. The double element softening curve is nonlinear and ends at 0.2 megapascal at 0.1 millimeter. The 768 and 2,592 element softening curves are nonlinear and end at 0.1 megapascal at 0.1 millimeter.

Figure 37. Illustration. The damage modes calculated in direct pull with a regulated softening formulation are in agreement for the basic and refined mesh simulations. This figure shows the damage in each mesh for four refinements: one element, two elements, basic mesh, and refined mesh. For one element, the damage is uniform top to bottom. For two elements, the damage dominates the top element. For the basic mesh, the damage is a single horizontal band located just above the vertical midplane. For the refined mesh, the damage is a single horizontal band located at the bottom row of elements. The damage is very similar to that calculated without regulation, and previously shown in Figure 33.

Figure 38. Graph. The stress-displacement curves calculated in unconfined compression with a regulated softening formulation nearly converge as the mesh is refined (fixed ends). The Y-axis is Stress in megapascals, and ranges from negative 65 to 0. The X-axis is Displacement in millimeters, and ranges from 0 to 3.8. Four curves are shown for four element sizes. The single element curve is nearly linear and decreases from the origin to negative 65 megapascals at 0.7 millimeter. The other three curves are linear to a peak of 46 megapascals at 0.42 millimeter. The two elements curve softens gradually to 0 megapascal at 1.6 millimeters. The 768 elements curve softens with more ductility, and reaches a plateau of negative 28 megapascals at 3.8 millimeters. The 2,592 elements curve softens with the most ductility, and reaches a plateau of negative 28.5 megapascals at 3.8 millimeters.

Figure 39. Illustration. The X-shaped damage mode calculated in unconfined compression with a regulated softening formulation is similar for the basic and refined mesh simulations (fixed ends). This figure shows the damage in each mesh for four refinements: one element, two elements, basic mesh, and refined mesh. For one and two elements, the damage is uniform top to bottom. For two elements, a bulge is evident at the vertical midplane. For the basic and refined meshes, the damage is two diagonal bands in the form of an X located about the vertical midplane. The damage bands for the refined mesh are narrower and more distinct than those of the basic mesh. The damage modes are very similar to those previously shown in Figure 35.

Figure 41. Graph. The stress-displacement curves calculated in unconfined compression without a regulated softening formulation become more brittle as the mesh is refined (fixed ends). The Y-axis is Stress in megapascals, and ranges from negative 65 to 0. The X-axis is Displacement in millimeters, and ranges from 0 to 3.8. Five curves are shown for five element sizes. The single element curves is nearly linear and decreases from the origin to negative 65 megapascals at 0.7 millimeter. The other four curves are linear to a peak of 46 megapascals at 0.42 millimeter. The two element curve softens gradually to negative7.5 megapascals at 3.8 millimeters. The 768 elements curve softens with more brittleness at first, but then reaches a plateau of negative 21 megapascals at 3.8 millimeters. The 2,592 elements curve softens with even more brittleness at first, but then reaches a plateau of negative 19.5 megapascals at 3.8 millimeters. The 6,144 elements curve softens with the most brittleness at first, but then reaches a plateau of negative 19.4 megapascals at 3.8 millimeters.

Figure 42. Graph. The stress-displacement curves calculated in unconfined compression with a regulated softening formulation become more ductile as the mesh is refined (fixed ends). The Y-axis is Stress in megapascals, and ranges from negative 65 to 0. The X-axis is Displacement in millimeters, and ranges from 0 to 3.8. Five curves are shown for five element sizes. The single element curves is nearly linear and decreases from the origin to negative 65 megapascals at 0.7 millimeter. The other three curves are linear to a peak of 46 megapascals at 0.42 millimeter. The two elements curve softens gradually to 0 megapascal at 1.6 millimeters. The 768 elements curve softens with more ductility, and reaches a plateau of negative 28 megapascals at 3.8 millimeters. The 2,592 elements curve softens with even more ductility, and reaches a plateau of negative 28.5 megapascals at 3.8 millimeters. The 6,144 elements curve softens with the most ductility, then reaches a plateau of negative 29 megapascals at 3.8 millimeters.

Figure 45. Illustration. The damage simulated in the full-scale beam is more severe than that simulated in the one-third-scale beam, which is consistent with the size effect. This figure shows six deformed configurations of the beams with damage. Three are for the full-scale beam, and three are for the one-third-scale beam. The times and relative deflections are 10 milliseconds with a relative deflection of 0.073, 20 milliseconds with a relative deflection of 0.127, and 30 milliseconds with a relative deflection of 0.22. Relative deflection is indicated as lowercase U divided by D. For each size beam, damage fringes form on the tensile face and extend towards the compressive face. They indicate tensile and shear cracks. For each beam, the fringes become stronger with time. The fringes for the one-third-scale beam are more densely populated than for the full-scale beam, indicating that less damage is experienced by the full-scale beam.

Figure 46. Graph. The stress-deflection behavior of the full-scale beam is softer than that of the one-third-scale beam, which is consistent with the size effect. The Y-axis is Stress in megapascals. It ranges from 0 to 2.7 megapascals. The X-axis is relative deflection defined as lowercase U divided by D. It ranges from 0 to 0.22. Two computed curves are shown: one for the full-scale beam, and the other for the one-third-scale beam. Both curves initiate at the origin. The full-scale beam curve rises to a peak of 1.8 megapascals at a relative deflection of 0.14, in a nonlinear manner. Then it softens slightly to 1.55 megapascals at a relative deflection of 0.21. The one-third-scale beam curve does not soften. Instead it rises to a peak of 2.45 megapascals at a relative deflection of 0.21, in a nonlinear manner.

Figure 47. Illustration. Without regulation of the softening formulation, the damage simulated in the full-scale and one-third-scale beams is nearly the same, which is inconsistent with the size effect. This shows one deformed configuration with damage of the full and one-third-scale beams. Both are shown at 30 milliseconds at a relative deflection of 0.22. Relative deflection is indicated by lowercase U divided by D. For each size beam, damage fringes form on the tensile face and extend towards the compressive face. They indicate tensile and shear cracks. The damage fringes for both beams are identical.

Figure 48. Graph. Without regulation of the softening formulation, the stress versus relative deflection curves of the full and one-third-scale beams are nearly identical, which is inconsistent with the size effect. The Y-axis is Stress in megapascals. It ranges from 0 to 2.7. The X-axis is relative deflection defined as lowercase U divided by D. It ranges from 0 to 0.22. Two computed curves are shown, one for the full-scale beam, and the other for the one-third-scale beam. Both curves initiate at the origin and are identical. They rise to a peak of 2.1 megapascals at a relative deflection of 0.20, in a nonlinear manner. Then they soften slightly.

Figure 49. Drawing. Sketch of four-point bend tests, showing dimensions in millimeters. This is a sketch of the one-third-scale beam tested in four-point bending. The beam is shown with steel reinforcement near the tensile face. The beam is supported on its end by two pinned constraints. The beam is loaded by two cylinders connected together by a plate, with an arrow showing the downward direction of loading. The horizontal dimension of the beam from one edge support to the loading point is 660.4 millimeters. The distance between loading points is 203.2 millimeters.

Figure 54. Illustration. The plain concrete beam initially breaks into three large pieces in all baseline calculations performed (shown at 12 milliseconds for impact at 5.8 meters per second (19.0 feet per second). The computed damage, deflection, and erosion of one plain concrete beam are shown. Damage is two major cracks beneath each impactor point, which breaks the beam into three major pieces. Fringes, without erosion, are also evident on the compressive face about one-fourth of the horizontal way from each beam end. Slight fringes are evident beneath on each end, on the compressive face, where beam elements tie down each end.

Figure 55. Illustration. The plain concrete beam ultimately breaks into five pieces in three of four calculations performed (shown at 26 milliseconds for impact at 5.8 meters per second (19.0 feet per second). The computed damage, deflection, and erosion of one plain concrete beam are shown. Damage is two major cracks beneath each impactor point, and two minor cracks one-fourth of the way from each end, which breaks the beam into five major pieces. Fringes are also evident on the compressive face about one-fourth of the horizontal way from each beam end. Slight fringes are evident beneath on each end, on the compressive face, where beam elements tie down each end.

Figure 56. Illustration.The plain concrete beam ultimately broke into four pieces in one of four calculations performed (shown at 26 milliseconds for impact at 5.0 meters per second (16.4 feet per second). The computed damage, deflection, and erosion of one plain concrete beam are shown. Damage is two major cracks beneath each impactor point, and one minor crack one-fourth of the way from one end, which breaks the beam into four major pieces. Fringes are also evident on the compressive face about one-fourth of the horizontal way from each beam end. Slight fringes are evident beneath on each end, on the compressive face, where beam elements tie down each end.

Figure 58. Photo. The over-reinforced concrete beam has localized tensile cracks and concrete crushing in the impactor regime (test 15 conducted at 5 meters per second (16.4 feet per second)). This is a post-test photo of the central portion of an over-reinforced concrete beam. Two arrows are drawn to indicate the location of the impactors. A tape measure is placed on top of the beam to show the relative scale. Approximately 6 inches are indicated between arrows. The beam damage is five prominent tensile or shear cracks originating on the tensile face and extending towards to the compressive face. Two of these cracks are evident on the top compressive face, as is compressive damage in the impactor region.

Figure 59. Illustration. The damage mode of the over-reinforced concrete beam at peak deflection is localized tensile cracks and concrete crushing in the impactor regime (shown at 16 milliseconds for impact at 5 meters per second (16.4 feet per second)). The computed damage is shown in one over-reinforced beam. The beam is bent in flexure, and rests on two half cylinder supports on each end. Two half cylinder impactors load the beam, with arrows showing the direction of impact. Shown are about 20 fringes, originating on the tensile face and extending vertically towards the compressive face, in the central impact regime. They indicate tensile cracks. Also, about one-fourth of the way from each end, fringes originate on the tensile face and extend diagonally towards the central compressive face. They indicate shear cracks.

Figure 60. Illustration. The simulated damage fringes for impact at 10.6 meters per second (34.8 feet per second) are less extensive than those simulated at 5.0 meters per second (16.4 feet per second). The computed damage is shown in one over-reinforced beam. The beam is bent in flexure, and rests on two half cylinder supports on each end. Two half cylinder impactors load the beam, with arrows showing the direction of impact. Shown are about 10 fringes, originating on the tensile face and extending vertically towards the compressive face, in the central impact regime. They indicate tensile cracks. Also, about one-fourth of the way from each end, fringes originate on the tensile face and extend diagonally towards the central compressive face. They indicate shear cracks.

Figure 61. Graph. The measured displacement histories are accurately simulated by LS-DYNA concrete material model MAT 159. The Y-axis is Displacement in millimeters, and ranges from negative 35 to 0. The X-axis is Time in seconds, and ranges from 0 to 0.02. Seven curves are shown; four for the calculations and three for the corresponding tests. The first simulation was conducted for a 14.5-kilogram impactor at 10.8 meters per second. The displacement history originates at 0,0 and peaks at about negative 18 millimeters at 0.006 second. Then it slowing rebounds to negative 7 millimeters at 0.02 second. No measured curve is available for comparison. The second simulation was conducted for a 31.75-kilogram impactor at 7.3 meters per second. The displacement history originates at 0,0 and peaks at about negative 24 millimeters at 0.011 second. Then it slowly rebounds to negative 16 millimeters at 0.02 second. The measured curve is similar, although it peaks at about 25 millimeters. The third simulation was conducted for a 47.86-kilogram impactor at 6.0 meters per second. The displacement history originates at 0,0 and peaks at about negative 28 millimeters at 0.013 second. Then it slowly rebounds to negative 22.5 millimeters at 0.02 second. The measured curve is similar, although it peaks at about 24 millimeters. The fourth simulation was conducted for a 63.93-kilogram impactor at 5.2 meters per second. The displacement history originates at 0,0 and peaks at about negative 30 millimeters at 0.015 seconds. Then it slowly rebounds to negative 28 millimeters at 0.02 seconds. The measured curve is similar, although it peaks at about 29 millimeters.

Figure 62. Graph. The processed velocity histories drift once the impactor separates from the beam during rebound at about 17 milliseconds. The Y-axis is Velocity in meters per second, and ranges from negative 8 to 2. The X-axis is Time in seconds, and ranges from 0 to 0.03. Six curves are shown. Three are computed, and three are from the corresponding tests. The calculations and tests are for 31.75 kilograms at 6.84 meters per second, 47.86 kilograms at 5.87 meters per second, and 63.93 kilograms at 5.0 meters per second. The three sets of curves originate between about negative 7 and negative 5 meters per second, then drop rapidly and plateau at about negative 3 meters per second until 0.007 seconds. At this time, all three sets of curves drop from negative 3 to about 1 meter per second within 0.015 to 0.025 seconds. Up to this point, the computed and measured curves are in very good agreement. But then they diverge. The computed curves remain at a constant velocity of about 1 meter per second, while the measured curves drop down into negative velocities. This indicates that the measured curves have drifted.

Figure 64. Illustration. The damage mode simulated for all under-reinforced beam specimens is two major cracks beneath the impactor points, with additional damage toward the ends the the beam. The computed damage is shown in one under-reinforced beam. The beam is bent in partial flexure, and rests on two half cylinder supports on each end. Two half cylinder impactors load the beam, with arrows showing the direction of impact. Shown are two regions of erosion, one beneath each impactor point. The erosion originates on the tensile face and extending vertically towards the compressive face, but does not quite break through the entire beam. Some pieces of concrete are falling away from the eroded region. The erosion reveals the intact reinforcement.

Figure 66. Graph. Good displacement history and peak deflection comparisons of LS-DYNA drop tower impact simulations with test data for plain and reinforced concrete beams. The Y-axis is Deflection in millimeters, and ranges from negative 150 to 0. The X-axis is Time in milliseconds, and ranges from 0 to 0.1. Three calculated curves are shown. The first is for an over-reinforced beam. It has the smallest deflection at about 26 millimeters at about 0.014 millisecond, then rebounds slightly. It is compared with one measured curve, which is quite similar. The second calculated curve is for an under-reinforced beam. It has a larger deflection, which is at 132 millimeters at about 0.065 millisecond, before it rebounds slightly. This deflection is slightly less than the measured deflections of 136 to 144 millimeters. The third curve is for a plain beam. It does not rebound. The curve is linear to 150 millimeters deflection at about 0.036 millisecond.

Figure 69. Photo. The beam tested at an impact velocity of 33.1 kilometers per hour (20.5 miles per hour) exhibits inclined shear cracks, localized crushing, and bond failure. Two snapshots from videos of the test are shown, both looking down on the top of the beam just after impact by the bogie vehicle. One is at 8 milliseconds, the other at 48 milliseconds. At 8 milliseconds, localized crushing is barely visible at the impactor points. Inclined shear cracks are prominent in the central portion of the beam, extending through the depth. By 48 milliseconds, bond failure between the reinforcement and concrete is evident near the end regions of the beam. The beam is breaking into three or four major pieces, with the central piece forming a wedge-like shape.

Figure 70. Illustration. Inclined shear cracks, localized crushing, and bond failure are simulated in the calculation conducted at 33 kilometers per hour (20.5 miles per hour). The computed response shows the deformed configuration, damage fringes, and erosion at three times, all looking down on the top of the beams just like the videos. At 8 milliseconds, wedge-shaped fringes form at each impactor point and extend across the depth of the beam. Inclined shear fringes also form about one-fourth of the way from each edge. At 48 milliseconds, erosion occurs at-angle, extending from each impactor point on the compression face toward the one-fourth point on the tensile face. This forms a central piece with a wedge-like shape, just like in the test. Bond failure between the reinforcement and concrete is evident near the end regions of the beam, just like in the test. At 80 milliseconds, the beam has effectively broken into three major pieces, with bond failure extending all the way out to the edges of the beam.

Figure 73. Illustration. Tensile damage, inclined shear damage, and bond failure are simulated in the calculation conducted at 15.9 kilometers per hour (9.9 miles per hour) with erosion set to 10 percent strain. The computed response shows the deformed configuration, damage fringes, and erosion at three times, all looking down on the top of the beam just like the videos. At 8 milliseconds, tensile and inclined shear fringes form on the tensile face and extend towards the compressive face, and cover about two-thirds of the beam. At 104 milliseconds, tension-side spall is evident in the central region. At 240 milliseconds, the beam has rebounded, although the spall is still evident. The beam remains intact, except for the spall.

Figure 74. Illustration. The beam breaks into two major pieces, and does not rebound when impacted at 18 kilometers per hour (11.2 miles per hour). The computed response shows the deformed configuration, damage fringes, and erosion at three times, all looking down on the top of the beam just like the videos. At 8 milliseconds, tensile and inclined shear fringes form on the tensile face and extend towards the compressive face, and cover about two-thirds of the beam. At 104 milliseconds, tension-side spall is evident in the central region, as well as erosion on the compressive face between the two impactor points. At 240 milliseconds, the erosion extends through the thickness of the beam, with slight debonding along the reinforcement. This effectively breaks the beam into two pieces.

Figure 75. Illustration. This damage modeled at 15.9 kilometers per hour (9.9 miles per hour) with erosion set to 1 percent strain is more extensive than when erosion is set to 10 percent strain. The computed response shows the deformed configuration, damage fringes, and erosion at three times, all looking down on the top of the beam just like the videos. At 8 milliseconds, tensile and inclined shear fringes form on the tensile face and extend towards the compressive face. Significant tensile and shear crack erosions occur in the central regime. Shear crack erosion occurs about one-fourth of the way from each end of the beam. A blowup of the erosion in the central regime indicates that the tensile cracks form on the tensile surface and extend about three-fourths of the way to the impactors. Slight erosion occurs beneath the impactors. At 104 milliseconds, the beam is beginning to break into five major pieces. At 160 milliseconds, significant debonding occurs along the reinforcement.

Figure 76. Photo. Cracks form on the tensile face of the beam impacted at 8.6 kilometers per hour (5.3 miles per hour), and propagate toward the compression face. Two snapshots from an overhead video are shown: one at 60 milliseconds, the other at 200 milliseconds. At 60 milliseconds, the beam is bending in flexure, and tensile hairline cracks are visible in the central impact region, as well as slight impact damage beneath the impactors. At 200 milliseconds, the beam has gone into reverse flexture. The tensile cracks are still visible, but additional large cracks form on the compressive face beneath the impactor.

Figure 78. Illustration. The simulation of the beam impacted at 8.6 kilometers per hour (5.3 miles per hour) exhibits substantial damage, but retains its integrity and rebounds. Two views of computed damage are shown looking down on the beam as it rests on the supports. One view, at 64 milliseconds, shows fringes that cover about two-thirds of the beam, which remains intact and is not broken. A closeup of the central region is shown at 64 milliseconds, which shows dominate tensile fringes but no erosion. At 320 milliseconds, the beam is viewed in reverse flexture. It is still intact and not broken, and shows a gap between the beam and bogie vehicle impactors.

Figure 79. Graph. The displacement histories from the LS-DYNA bogie vehicle impact simulations compare well with the test data. The Y-axis is Displacement in millimeters, and ranges from negative 600 to 200. The X-axis is Time in milliseconds, and ranges from 0 to 0.32. Four sets of curves are shown. Three sets are measurements and calculations for the deflection of the beam. One set is measurements and calculations for the bogie vehicle. The first is for the Test 1 simulation conducted at 15.9 kilometers per hour. It originates at the origin, then peaks at about 210 millimeters in 0.1 millisecond, before rebounding to negative 90 millimeters at 0.24 millisecond. No measured curve is available for comparison. The second set of curves is for Test 2 conducted at 15.9 kilometers per hour. The measured curve originates at the origin, and is approximately linear to negative 600 millimeters at 0.076 millisecond. The computed curve is similar, but not identical. The third set of curves is for Test 3 conducted at 8.6 kilometers per hour. The measured curve originates at the origin, then peaks at about negative 70 millimeters at 0.07 millisecond before rebounding to a plateau of 50 millimeters at 0.32 millisecond. The computed curve is similar, but not identical. The fourth set of curves is for Test 3 conducted at 8.6 kilometers per hour, and is a measurement on the vehicle, rather than the beam. The measured curve originates at the origin, then peaks at about negative 70 millimeters at 0.07 millisecond before rebounding in a straight line to 140 millimeters at 0.32 millisecond. The computed curve is similar, but not identical.

Figure 80. Graph. The calculations conducted at 8.6 kilometers per hour (5.3 miles per hour) correlate best with the test data if the supports are modeled. The Y-axis is Displacement in millimeters, and ranges from negative 80 to 60. The X-axis is Time in milliseconds, and ranges from 0 to 0.32. Three curves are shown. One is a measured curve (test data). It originates at the origin and peaks at about 70 millimeters in 0.07 millisecond. Then it rebounds and plateaus at about 47 millimeters in 0.32 millisecond. The second curve is for the calculation conducted with supports. It is similar, but not identical to the measured curve. The third curve is for the calculation conducted without supports. It originates at the origin and peaks at about 70 millimeters in 0.07 millisecond. Then it rebounds, but does not plateau. Instead, it continues approximately linearly to 60 millimeters in 0.28 millisecond.

Figure 81. Graph. Strain histories measured on the compressive face of each beam peak around 0.23 percent strain. The Y-axis is Strain, and ranges from negative 0.0038 to 0. The X-axis is Time in milliseconds, and ranges from 0 to 0.24. Three measured curves are shown for Tests 1, 2, and 3. All three curves peak at about 0.23 percent strain, but take different paths to get there. Test 1 at 15.9 kilometers per hour peaks at about 0.03 millisecond, then drops back down to negative 0.0005 in 0.08 millisecond, where it remains. Test 2 at 33.1 kilometers per hour peaks at less than 0.01 millisecond, then drops back down to negative 0.0006 at 0.02 millisecond, before jumping back to negative 0.0018 at 0.04 millisecond. Test 3 at 8.6 kilometers per hour peaks at about 0.04 millisecond, remains there until 0.09 millisecond, then gradually drops back down to negative 0.0006 at 0.20 millisecond.

Figure 82. Graph. The strain histories from the LS-DYNA bogie vehicle impact simulations vary with impact velocity. The Y-axis is Strain, and ranges from negative 0.0038 to 0. The X-axis is Time in milliseconds, and ranges from 0 to 0.24. Three computed curves are shown, all with different peaks. Test 1 at 15.9 kilometers per hour peaks at negative 0.0038 at about 0.035 millisecond, then gradually drops back down to negative 0.0019 in 0.14 millisecond. The strain then drops back down to 0 in 0.21 millisecond, as the beam goes into reverse flexture. Test 2 peaks at negative 0.001 about 0.005 millisecond, then drops back down near 0 strain in 0.06 millisecond, where it remains. Test 3 peaks at negative 0.0021 in 0.03 millisecond, then drops back down to negative 0.0007 at 0.022 millisecond. Then the curve drops to 0 strain in 0.23 millisecond.

Figure 95. Graph. Force-time histories for benchmark tests and spring models. The Y-axis is Force in kilonewtons, and ranges from negative 140 to 20. The X-axis is Time in seconds and ranges from 0 to 0.15. Four curves are shown. One is for the rigid pole calibration test. The other is the fit of the original spring pendulum model to the measured curve. Both are similar, but not identical. They originate at the origin, and peak at about negative 128 kilonewtons in 0.08 seconds. Then the curves rapidly drop back to 0 kilonewton in about 0.12 seconds. The third curve is the measured curve for test P5. The fourth curve is the fit of the new spring pendulum model to the test P5 curve. Both curves are similar, but not identical. They originate at the origin, and peak at about negative 132 kilonewtons in 0.095 seconds. Then the curves rapidly drop back to 0 kilonewton in about 0.12 seconds. The measured curve is more oscillatory than the curve fit to it.

Figure 96. Graph. Force-displacement relationships for benchmark tests and SBP2 model. The Y-axis is Force in kilonewtons, and ranges from negative 160 to 20. The X-axis is Displacement in meters, and ranges from 0 to 0.7. Three curves are shown. One is the measured and derived curve for Test P5. The second curve is the calculated curve for Test P5, using the new spring model. Both curves are similar, although the measured curve is more oscillatory. The third curve is the measured and derived curve from the rigid pole test. Although all three curves peak at about negative 130 kilonewtons at 0.58 meter, the rigid pole curve lies below the other two curves, having less force at a given deflection.

Figure 99. Illustration. Closeup view of steel rail system with four-bolt anchorage. This is a closeup of the mesh of the rail supported by the two steel posts attached to the baseplate. Four bolts through the baseplate are also shown. The rail is a cylinder with an elliptical cross section with 24 shell elements along the length and 26 shell elements around the circumference. Each steel post is nine hex elements high, two hex elements thick, and five hex elements wide. The baseplate is 2 hex elements high, 21 hex elements thick, and 9 hex elements wide.

Figure 100. Illustration. Steel reinforcement and anchor bolts for T4 bridge rail specimen with four-bolt anchorage and 254-millimeters- (10-inch-) wide parapet. This is a closeup of the steel reinforcement in the parapet as it attaches to the deck. The four bridge rail anchor bolts protrude through the top of the parapet steel mesh. Vertical reinforcement in the parapet consists of 10 "V" bars spaced 266.6 millimeters apart. Longitudinal reinforcement consists of two steel bars equally spaced near the top of the parapet and within the "V" bars.

Figure 101. Illustration. Steel reinforcement and anchor bolts for T4 bridge rail specimen with three-bolt anchorage and 317.5-mm- (12.5-inch-) wide parapet. This is a closeup of the steel reinforcement in the parapet as it attaches to the deck. The three bridge rail anchor bolts protrude through the top of the parapet steel mesh. Vertical reinforcement in the parapet consists of 10 "V" bars spaced 266.6 millimeters apart. Longitudinal reinforcement consists of two steel bars equally spaced near the top of the parapet and within the "V" bars.

Figure 102. Illustration. Right end view of parapet-only model for four-bolt design and three-bolt design. Two side views of the mesh are shown. One is for the four-bolt design, and the other is for the three-bolt design. Each view shows the honeycomb front end of the bogie vehicle just before impact with the bridge rail. The honeycomb is three elements deep and three elements high. The cross section of each rail is elliptical. Each steel support post is five elements wide and nine elements high. The steel plate for the four-bolt design is nine elements wide and two elements high. The steel plate for the three-bolt design is 12 elements wide and 2 elements high. Both sit on top of the concrete parapet. The parapet for the four-bolt design is 16 elements wide and 29 elements high. The parapet for the three-bolt design is 20 elements wide and 20 elements high.

Figure 103. Illustration. Original parapet mesh used for merging nodes with steel reinforcement. The mesh of the steel reinforcement is shown within the concrete parpapet mesh. The nodes of the vertical and horizontal reinforcement bars are aligned with the nodes of the concrete hex elements. The size of the concrete hex elements varies with the width of the parapet, and is more refined in the region of the reinforcement. The size of the concrete hex elements also varies in the vertical direction, with smaller size elements near the top of the parapet where the reinforcement is concentrated.

Figure 107. Illustration. Boundary conditions used for the full system model with deck and for the parapet-only model. This figure shows two closeups of the mesh. One view shows the bottom of the parapet that is connected to the deck. The fixed edge of the deck is shown, with arrows pointing to the vertical and horizontal edges that are fixed. The arrows are accompanied by a note that says "Fixed left edge, left nodes of the horizontal reinforcement and bottom nodes of the deck." The second view shows the parapet only, with arrows pointing to the bottom edge of the parapet. The arrows are accompanied by a note that says "Fixed bottom nodes of the parapet and vertical reinforcement."

Figure 109. Illustration. Contacts definitions for the T4 bridge rail model. This is a view of the bridge rail, parapet, and deck, just before it is impacted by the nose of the bogie pendulum. Four contact surface locations are indicated by the labels with arrows. The first surface, labeled Nose and Rail, is between the honeycomb nose and bridge rail. The second surface, labeled Baseplate and Parapet, lies between the bottom of the baseplate and top of the concrete parapet. The third surface, labeled Parapet and Deck, lies between the bottom of the parapet and top of the concrete deck. The fourth surface, labeled Reinforcement (self), shows arrows pointing to the partially exposed reinforcement.

Figure 110. Illustration. Damage fringe for baseline simulation of T4 with four-bolt anchorage and 254-millimeter- (10-inch-) wide parapet. This figure shows damage fringes, which are primarily on top of the parapet, and located beneath the baseplate, which has been removed for better viewing. Small fringe lines extend down the back face of the parapet, and are located a distance apart that is the width of the baseplate. No erosion or other deformation is visible.

Figure 112. Illustration. Element erosion profile (simulation case02, erode equals 1) on field side. This view shows the computed erosion pattern on the field side of the parapet. Three lines or erosion are evident on the edge of the deck. The top of the parapet is heavily eroded. The field side of the parapet is slightly eroded, with two vertical lines extending from the top of the parapet down the back side of the parapet to midheight. The distance between the eroded lines is the approximate width of the baseplate.

Figure 113. Illustration. Damage fringes for simulation case02 (erode equals 1). This is a view of both the computed erosion and damage fringes. The erosion pattern is coincident with the damage fringe pattern, except the damage fringes extend beyond the erosion. Three lines of erosion and damage are evident on the top of the deck. The top of the parapet is heavily eroded and fringed. Two lines of erosion extend midway down the field side of the parapet, whereas the damage fringes extend down the entire height of the parapet.

Figure 114. Illustration. Parapet failure with fracture energies at 20 percent of baseline values. This is a view of the deformed configuration of the bridge rail as it is being struck by the pendulum. The first stage of honeycomb is nearly completely crushed. The honeycomb nose is pushed out over top of the rail. The rail has drastically deflected toward the field side. The baseplate rotates with the steel posts and rail, and pulls partially out of the parapet, which exposes the bolts in the broken concrete.

Figure 115. Graph. Energy-time histories for pendulum impact of T4 bridge rail with fracture energies at 20 percent of baseline values. The Y-axis is Energy in kilojoules, and ranges from 0 to 120. The X-axis is Time in seconds, and ranges from 0 to 0.18. Four curves are shown. Two curves initiate at the origin. One of these curves is for the concrete internal energy. It increases to a value of about 19 kilojoules in about 0.07 second, then remains constant at this value. The second of these curves is for the system internal energy. It increases to a value of about 93 kilojoules in about 0.12 second, then remains constant at this value. The other two curves originate at 38 kilojoules at 0 second. One of these curves is the system kinetic energy. It gradually drops in value to about 13 kilojoules in 0.06 second, then drops more slowly to 9 kilojoules in 0.016 second. The second of these curves is for the total system energy. It increases slightly to bout 42 kilojoules in 0.06 second, and then increases more rapidly to about 102 kilojoules in 0.16 second.

Figure 117. Illustration. Parapet failure with fracture energies at 27.5 percent of baseline values. This is a closeup view of the top center and field side of the parapet. The erosion pattern is confined to the top of the parapet, but is more extensive than previously shown in Figure 116. Three main horizontal rows of erosion are evident, and extend the width of the baseplate (which has been removed for better viewing). At each end of the central row and field edge row are at-angle lines of erosion.

Figure 118. Graph. Energy-time histories for pendulum impact of T4 bridge rail with fracture energies at 27.5 percent of baseline values. The Y-axis is Energy in kilojoules, and ranges from 0 to 70. The X-axis is Time in seconds, and ranges from 0 to 0.30. Four curves are shown. Two curves initiate at the origin. One of these curves is for the concrete internal energy. It increases to a value of about 18 kilojoules in about 0.1 second, then remains constant at this value. The second of these curves is for the system internal energy. It increases to a value of about 66 kilojoules in about 0.12 second, then remains constant at this value. The other two curves originate at 38 kilojoules at 0 second. One of these curves is the system kinetic energy. It gradually drops in value to about 0 kilojoule in 0.1 second. The second of these curves is for the total system energy. It increases slightly to about 40 kilojoules in 0.02 second, then increases more rapidly to about 67 kilojoules in 0.12 second.

Figure 119. Illustration. Enhanced anchor bolt-to-baseplate connection model. This is a closeup of the mesh of the baseplate with the four bolts protruding out the top and bottom. Also visible are four washers, which are located around the bolts on the top of the baseplate. A note is included which states: baseplate can slide vertically or rotate with respect to anchor bolts based on material strength of bolts and wasters. Two arrows extend from this note, one to the baseplate and the other to the bolt.

Figure 120. Illustration. Fracture profile of modified T4 system at 0.080 seconds. This is a view of the top and field side of the parapet which shows the deformed configuration at 0.08 second. The rail remains attached to the baseplate, which rotates relative to the top of the concrete parapet. A bulge within the concrete is highly visible down the field side of the parapet. Minor erosion is evident on the top of the parapet, extending at-angle from the bolt locations to the field edge.

Figure 124. Illustration. Fracture profile for T4 bridge rail with four-bolt anchorage for parapet and eroded elements. This is a closeup view of the top and traffic side of the parapet. Element erosion is on top of the parapet in two rows. The rows are the approximate width of the baseplate, which has been removed for better viewing. Also shown is a view of the eroded elements only, without the intact elements of the parapet. The traffic side row of elements extends six elements down into the parapet, which is about one-fourth of the height of the parapet. The field side row of elements extends 18 elements down into the parapet, which is about three-fourths of the height of the parapet.

Figure 125. Graph. Pendulum bogie accelerations for impact of T4 bridge rail with four-bolt anchorage and 254-millimeter- (10-inch-) wide parapet. The Y-axis is Acceleration in Gs, and ranges from negative 18 to 0. The X-axis is Time in seconds, and ranges from 0 to 0.3. Three curves are shown, all filtered with an SAE Class 180 filter. All three curves originate at the origin. One curve for test P03 increases to a peak of negative 17.5 Gs in 0.075 second then softens rapidly with oscillations to about negative 5 Gs in 0.1 second. It remains at negative 5 Gs until 0.5 second, then gradually decays to 0 Gs in 0.085 second. The second curve for test P04 increases to a peak of negative 15.5 Gs in 0.085 second then softens rapidly with oscillations to about negative 2 Gs in 0.1 second. It then gradually decays to 0 Gs in 0.20 second. The third curve for the LS-DYNA simulation increases to a peak of negative 15.5 Gs in 0.090 second then softens rapidly without oscillations to about 0 Gs in 0.14 second.

Figure 126. Graph. Pendulum bogie velocities for impact of T4 bridge rail with four-bolt anchorage and 254-millimeter- (10-inch-) wide parapet. The Y-axis is Velocity in meters per second, and ranges from negative 3 to 11. The X-axis is Time in seconds, and ranges from 0 to 0.3. Three curves are shown, all filtered with an SAE Class 180 filter. All three curves originate at 9,500 meters per second at 0 second. All three curves gradually decay, in a similar manner to about 2.3 meters per second in about 0.07 second. Then the three curves begin to differ. The first curve for test P03 softens gradually then plateaus at about negative 1.4 meters per second in 0.2 second. The second curve for test P04 softens more rapidly than for test P03, but then plateaus at a slightly higher value of negative 1 meter per second in 0.2 second. The third curve for the LS-DYNA simulation continues to soften more rapidly than the test measurements, and plateaus at negative 2.5 at about 0.14 second.

Figure 129. Illustration. Damage to 317.5-millimeter- (12.5-inch-) wide parapet after pendulum impact showing damage fringes. This is a closeup view of the top and traffic side of the parapet. Damage fringes are evident at the top of the parapet in the region of the baseplate, which has been removed for better viewing. Two vertical rows of damage fringes also extend down the field side of the parapet. The spacing between the vertical rows is the approximate width of the baseplate.

Figure 130. Graph. Pendulum bogie accelerations for impact of T4 bridge rail with three-bolt anchorage and 317.5-millimeter- (12.5-inch-) wide parapet. The Y-axis is Acceleration in Gs, and ranges from negative 22 to 0. The x-axis is Time in seconds, and ranges from 0 to 0.3. Three curves are shown, all filtered with an SAE Class 180 filter. All three curves originate at the origin. One curve for test P05 increases to a peak of negative 16 Gs in 0.09 second, then softens rapidly without oscillations to 0 Gs in 0.125 seconds. The second curve for test P07 increases to a peak of negative 21 Gs in 0.08 second, then softens rapidly with little oscillation to 0 Gs in 0.125 second. The third curve for the LS-DYNA simulation increases to a peak of negative 15.5 Gs in 0.095 second then softens rapidly without oscillations to about 0 Gs in 0.135 second.

Figure 131. Graph. Pendulum bogie velocities for impact of T4 bridge rail with three-bolt anchorage and 317.5-millimeter- (12.5-inch-) wide parapet. The Y-axis is Velocity in meters per second, and ranges from negative 3 to 11. The X-axis is Time in seconds, and ranges from 0 to 0.3. Three curves are shown, all filtered with an SAE Class 180 filter. All three curves originate at 9.5 meters per second at 0 second, and are similar, but not completely identical. All three curves gradually decay to about negative 2 meters per second in about 0.11 second. Then the three curves plateau and remain constant at negative 2 meters per second for the remainder of the test or simulation.

Figure 133. Photo. Failure mode at end of the safety-shaped barrier. This figure is a closeup of the region of testing of the parapet. It shows the steel spreader plate attached to the timber. The timber and plate are clamped to the front and back faces of the parapet at the top right hand corner (when facing the parapet). The plate and timber load the parapet horizontally. The damage mode is primarily a crack which initiates midheight where the barrier transitions from thin to thick. This crack forms on the front loaded face and arcs downward towards the back edge of the parapet where it joins up with the deck. Inclined shear cracks are also present on the front loaded face beneath the region of load application.

Figure 134. Graph. Measured load versus displacement for the safety-shaped barrier. The Y-axis is Force in units of kilonewtons. It ranges from 0 to 355.9 kilonewtons. The X-axis is displacement in millimeters. It ranges from 0 to 76.2 millimeters. One curve is shown for the measured data. The force increases from 0, in a nonlinear manner, to a peak of 156 kilonewtons at a displacement of about 10 millimeters. Then the curve softens, somewhat linearly, to about 20 kilonewtons at 64 millimeters.

Figure 135. Illustration. Cross section of the Florida safety-shaped Barrier with New Jersey profile. This figure shows details of the steel reinforcement and concrete. The vertical reinforcement in the parapet are number 4 bars, with a 50.8 millimeters cover. All longitudinal reinforcement are number 4 bars. The reinforcement in the exisiting concrete are number 5 bars. A 6.35 millimeters plate is welded to the existing rebar and to the new hook bars. The reinforcement extends down from the existing concrete as number 5 bars.

Figure 136. Illustration. Cross section of Florida barrier model concrete mesh and reinforcement layout. This figure shows the mesh of the concrete and reinforcement used in the LS-DYNA calculation of the safety-shaped barrier. The concrete mesh is for the parapet and deck. The parapet is 8 elements wide at the top, transitioning to 16 elements wide at the bottom. There are 32 elements in the vertical direction. The deck is 24 elements wide and 7 elements deep. The reinforcement model consists of horizontal reinforcement in both the deck and parapet. Also shown are numerous stirrups in the top thin half of the parapet, and another set of stirrups in the bottom, thicker half of the parapet, which connect the parapet to the deck.

Figure 140. Illustration. A damage concentration is simulated in the parapet due to application of the steel/timber spreader that is not observed in the post-test parapet. This figure shows the damage fringes in the parapet. A large concentration of damage occurs where the timber contacts the parapet. Such unexpected contact damage is not visible in the test specimen. The figure also highlights this damage concentration region, and magnifies this region for better viewing by the reader. A gap between the timber and parapet is visible.

Figure 141. Illustration. The damage concentration is relieved if the timber is realistically modeled as an elastoplastic damaging material. This figure shows two views of the safety-shaped barrier at 16.5 millimeters and 38.1 millimeters of displacement. At 16.5 millimeters, the damage fringes are light, and no erosion is visible. At 38.1 millimeters, the damage fringes increase in intensity, and erosion occurs in three places. The primary erosion is a horizontal split on the loading face of the barrier at midheight, where the barrier transitions from thick to thin. Slight erosion also occurs to the side of where the timber pushes against the parapet. Unexpected erosion occurs on the loading face of the parapet, midheight between the deck and the thick-to-thin transition region. This unexpected damage is not visible in the test specimen.

Figure 142. Illustration. A realistic damage and erosion pattern is simulated if the timber remains in contact with the parapet (erode equals 1.05). This figure shows two views of the safety shaped barrier at two different angles when the applied displacement is 20 millimeters, and erode equals 1.05. The first view, plotted with the mesh turned on, reveals the eroded crack pattern. Erosion is primarily a horizontal split halfway through the barrier at midheight, where the barrier transitions from thick to thin. The second view, plotted with the mesh turned off, reveals the damage fringes for the eroded crack pattern. These are mainly inclined shear fringes on the loaded face of the barrier. In both cases, no gap is noted between the timber and parapet. The element representing the ram face is also shown on the center of the steel spreader plate attached to the timber.

Figure 143. Illustration. The primary erosion agrees with the measured crack pattern if the timber remains in contact with the parapet (erode equals 1.0). This figure shows two views of the safety shaped barrier at two different angles when the applied displacement is 10 millimeters and erode equals 1.0. The first view, plotted with the mesh turned on, reveals the eroded crack pattern. Erosion is primarily a horizontal split halfway through the barrier, which arcs towards the backface (side not loaded) of the barrier. Small tensile erosion cracks are also visible in the deck in the vicinity of the joint. The second view, plotted with the mesh turned off, reveals the damage fringes for the eroded crack pattern. In both cases, no gap is noted between the timber and parapet.

Figure 144. Illustration. The primary erosion agrees with the measured crack pattern if the timber remains in contact with the parapet (erode equals 1.0). This figure shows two views of the safety shaped barrier at two different angles when the applied displacement is 20 millimeters and erode equals 1.0. The first view, plotted with the mesh turned on, reveals the eroded crack pattern. This includes inclined shear cracks beneath the region of load application, and a horizontal split halfway through the barrier, which arcs towards the backface (side not loaded) of the barrier. Small tensile erosion cracks are also visible in the deck in the vicinity of the joint. The second view, plotted with the mesh turned off, reveals the damage fringes, particularly the inclined shear cracks. In both cases, no gap is noted between the timber and parapet. The erosion is much more extension with erode equals 1.0 than when erode equals 1.05.

Figure 145. Graph. The calculated force versus deflection history is in reasonable agreement with the measured curve for the first 12 millimeters (0.5 inches) of deflection. The Y-axis is force in units of kilonewtons. It ranges from 0 to 200. The X-axis is displacement in units of millimeters. It ranges from 0 to 30. Two curves are shown. The solid line is for the test data. It increases in a nonlinear manner from 0 force and displacement to a peak force of 156 kilonewtons at a displacement of about 10 millimeters. Then the data curve softens to about 115 kilonewtons at 22 millimeters. The dashed line is for the LS-DYNA calculation. It is similar to the data curve to up to 10 millimeters of displacement. However, the calculation force keeps increasing while the test curve softens. The calculation increases to a force of about 180 kilonewtons at a displacement of 30 millimeters.

Figure 146. Illustration. The computed damage mode is similar to that measured if the load is applied via concentrated nodal point forces (at 11- to 12-millimeter (0.43- to 0.5-inch) deflection). This figure compares the damage generated in the safety-shaped barrier when erode equals 1.05 compared with erode equals 1.0. Both inclined shear cracks and erosion are present in the region of load application. However, the erosion is more extensive when erode equals 1.0 than when erode equals 1.05.

Figure 147. Graph. The computed force versus displacement unloads, when the load is applied via concentrated nodal point forces (erode equals 1.05). The Y-axis is Force in kilonewtons. It ranges from 0 to 160. The X-axis is displacement in millimeters. It ranges from 0 to 12. One curve is shown, beginning at 0 force and displacement, and increasing in a nonlinear manner to about 155 kilonewtons at 11.5 millimeters. Then the curve unloads in a linear manner to about 78 kilonewtons at 9.5 millimeters.

Figure 162. Illustration. Plain conrete damage fringe at 20 milliseconds (developer). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. Erosion, all the way through the beam thickness, is also evident beneath each impactor point, which effectively breaks the beam into three pieces.

Figure 163. Illustration. Plain conrete damage fringe at 30 milliseconds (developer). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. Extensive erosion, all the way through the beam thickness, is evident beneath each impactor point. Smaller erosion cracks are also evident within the fringes one-fourth of the distance from each end. The beam is effectively broken into three pieces.

Figure 165. Illustration. Plain concrete damage fringe lowercase T equals 4 milliseconds (user Linux). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. Erosion, part way through the beam thickness, is also evident beneath each impactor point. The damage is nearly identical to that calculated by the developer.

Figure 166. Illustration. Plain concrete damage fringe lowercase T equals 20 milliseconds (user Linux). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. Erosion, all the way through the beam thickness, is also evident beneath each impactor point, which effectively breaks the beam into three pieces. The damage is nearly identical to that calculated by the developer.

Figure 167. Illustration. Plain concrete damage fringe lowercase T equals 30 milliseconds (user Linux). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. Extensive erosion, all the way through the beam thickness, is evident beneath each impactor point. Smaller erosion cracks are also evident within the fringes one-fourth of the distance from each end. The beam is effectively broken into three pieces. The damage is nearly identical to that calculated by the developer.

Figure 169. Illustration. Plain concrete damage fringe lowercase T equals 4 milliseconds (user Windows). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. Erosion, part way through the beam thickness, is also evident beneath each impactor point. The damage is nearly identical to that calculated by the developer.

Figure 170. Illustration. Plain concrete damage fringe lowercase T equals 20 milliseconds (user Windows). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. Erosion, all the way through the beam thickness, is also evident beneath each impactor point, which effectively breaks the beam into three pieces. The damage is nearly identical to that calculated by the developer.

Figure 171. Illustration. Plain concrete damage fringe lowercase T equals 30 milliseconds (user Windows). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. Extensive erosion, all the way through the beam thickness, is evident beneath each impactor point. Smaller erosion cracks are also evident within the fringes one-fourth of the distance from each end. The beam is effectively brokent into three pieces. The damage is nearly identical to that calculated by the developer.

Figure 178. Illustration. Reinforced concrete damage fringe lowercase T equals 16 milliseconds (user Linux). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested in the drop tower facility. Damage fringes are concentrated in the central region, but also spread out and join those previously formed at one-fourth of the distance from each end of the beam. The beam is deflecting in flexure. The damage is nearly identical to that calculated by the developer.

Figure 179. Illustration. Reinforced concrete damage fringe lowercase T equals 20 milliseconds (user Linux). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested in the drop tower facility. Damage fringes are concentrated in the central region, but also spread out and join those previously formed at one-fourth of the distance from each end of the beam. The beam is deflecting in flexure, but has started to rebound. The damage is nearly identical to that calculated by the developer.

Figure 182. Illustration. Bogie damage, lowercase T equals 4 milliseconds (developer). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out and join those previously formed at one-fourth of the distance from each end of the beam. Slight erosion is evident just beneath the impactors. Slight lines of erosion also originate on the compressive face, one-fourth of the distance from each end of the beam. They extend about halfway through the thickness of the beam.

Figure 183. Illustration. Bogie damage, lowercase T equals 8 milliseconds (developer).
This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Slight erosion is evident just beneath the impactors. Slight lines of erosion also originate on the compressive face, about one-fourth of the distance from each end of the beam. They extend through the thickness of the beam to the reinforcement on the tensile face. At the reinforcement, slight debonding between the concrete and reinforcement is evident.

Figure 184. Illustration. Bogie damage, lowercase T equals 48 milliseconds (developer). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Erosion is still evident just beneath the impactors. Definite lines of erosion also originate on the compressive face in about six places. They extend through the thickness of the beam to the reinforcement on the tensile face. At the reinforcement, significant debonding between the concrete and reinforcement is evident.

Figure 185. Illustration. Bogie damage, lowercase T equals 80 milliseconds (developer). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Erosion is still evident just beneath the impactors. Definite lines of erosion also originate on the compressive face in about six places. They extend through the thickness of the beam to the reinforcement on the tensile face. At the reinforcement, the debonding between the concrete and reinforcement has grown. The beam is highly deflected, and has pulled away from the load frame cylinders.

Figure 186. Illustration. Damage fringe lowercase T equals 4 milliseconds (user Windows). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Slight erosion is evident just beneath the impactors. Slight lines of erosion also originate on the compressive face, about one-fourth of the distance from each end of the beam. They extend about halfway through the thickness of the beam. The damage is nearly identical to that calculated by the developer.

Figure 187. Illustration. Damage fringe lowercase T equals 8 millisecond s (user Windows). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Slightly more erosion than previously shown at 4 milliseconds is evident just beneath the impactors. Definite lines of erosion also originate on the compressive face, about one-fourth of the distance from each end of the beam. They extend through the thickness of the beam to the reinforcement on the tensile face. At the reinforcement, slight debonding between the concrete and reinforcement is evident. The damage is nearly identical to that calculated by the developer.

Figure 188. Illustration. Damage fringe lowercase T equals 48 millisecond s (user Windows). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Erosion is still evident just beneath the impactors. Definite lines of erosion also originate on the compressive face in about four places. They extend through the thickness of the beam to the reinforcement on the tensile face. At the reinforcement, significant debonding between the concrete and reinforcement is evident. The damage is similar to that calculated by the developer.

Figure 189. Illustration. Damage fringe lowercase T equals 80 millisecond s (user Windows). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Erosion is still evident just beneath the impactors. Definite lines of erosion also originate on the compressive face in about four places. They extend through the thickness of the beam to the reinforcement on the tensile face. At the reinforcement, the debonding between the concrete and reinforcement has grown. The beam is highly deflected, and has pulled away from the load frame cylinders. The damage is similar to that calculated by the developer.

Figure 190. Illustration. Damage, lowercase T equals 4 millisecond s (user Linux). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Slight erosion is evident just beneath the impactors. Slight lines of erosion also originate on the compressive face, about one-fourth of the distance from each end of the beam. They extend about halfway through the thickness of the beam. The damage is nearly identical to that calculated by the developer, and identical to that calculated with user Windows.

Figure 191. Illustration. Damage, lowercase T equals 8 millisecond s (user Linux). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Slightly more erosion is evident just beneath the impactors. Definite lines of erosion also originate on the compressive face, about one-fourth of the distance from each end of the beam. They extend through the thickness of the beam to the reinforcement on the tensile face. At the reinforcement, slight debonding between the concrete and reinforcement is evident. The damage is nearly identical to that calculated by the developer, and identical to that calculated with user Windows.

Figure 192. Illustration. Damage, lowercase T equals 48 millisecond s (user Linux). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Definite lines of erosion also originate on the compressive face in about four places. They extend through the thickness of the beam to the reinforcement on the tensile face. At the reinforcement, significant debonding between the concrete and reinforcement is evident. The damage is similar to that calculated by the developer, and identical to that calculated with user Windows.

Figure 193. Illustration. Damage, lowercase T equals 80 millisecond s (user Linux). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested by bogie vehicle impact. Damage fringes are concentrated in the central region, but also spread out to join those previously formed at one-fourth of the distance from each end of the beam. Erosion is still evident just beneath the impactors. Definite lines of erosion also originate on the compressive face in about four places. They extend through the thickness of the beam to the reinforcement on the tensile face. At the reinforcement, the debonding between the concrete and reinforcement has grown from 48 milliseconds. The beam is highly deflected, and has pulled away from the load frame cylinders. The damage is similar to that calculated by the developer, and identical to that calculated with user Windows.

Figure 194. Illustration. Finite element model of the pendulum, rail, and fixed end of parapet. This figure shows the complete LS-DYNA model of the pendulum impacting the bridge rail. One end of the spring is attached to the movable pendulum case. The other end is attached to a steel plate adjacent to a honeycomb nose. The honeycomb nose is about to impact the elliptical steel rail, which is attached via steel supports to a steel baseplate. The baseplate is bolted to the top of the reinforced concrete parapet. The bottom end of the parapet is a fixed end. Also shown is a view of the pendulum with the movable pendulum case removed, which reveals concentrated mass inside.

Figure 195. Illustration. Damage fringes calculated with baseline properties for a fixed end parapet. This figure shows a side view of the pendulum impacting the rail, which reveals that the honeycomb crushes up about 75 percent. Little lateral deflection is visible. Also shown is a closeup view of the top of the parapet, with the rail and baseplate removed. Slight erosion damage extends along the top center of the parapet. Its horizontal extension is about the width of the steel plate. At each end of this crack are inclined shear fringes, without erosion, running from the center to back face of the parapet. Slight damage fringes extend down the back face of the parapet.

Figure 196. Illustration. The deformed configuration and damage of the Texas T4 bridge rail (four-bolt design) from impact with the simplified pendulum model (without a crushable nose) at 25 percent maximum available kinetic energy is similar to that observed during the tests. This figure shows a side view of the simplified pendulum impacting the rail. The simplified pendulum is the exact geometric size of the honeycomb nosecone, only the honeycomb material model has been replaced with elastic steel, and the entire mass of the pendulum is concentrated in the steel. About 100 millimeters of rail deflection is visible, similar to that seen in one test. Also shown is a closeup view of the top of the parapet, with the rail and baseplate removed. Substantial erosion damage extends along the top center of the parapet, which splits open the parapet. Its horizontal extension is about the width of the steel plate. At each end of this large crack are eroded inclined shear cracks running from the center to back face of the parapet. Erosion and damage fringes extend down the back face of the parapet.

Figure 197. Graph. Stiffening the spring increases the maximum deceleration and decreases the time at which the maximum deceleration occurs. The Y-axis is acceleration in units of millimeters per second. It ranges from negative 280,000 to 0 millimeters per second. The X-axis is time in units of seconds. It ranges from 0 to 0.15 second. Four calculated curves are shown. The first curve, which is dotted, is for baseline concrete properties with original spring stiffness, labeled 100 percent. This curve decreases from 0 to negative 180,000 millimeters per second in about 0.09 second, then decays rapidly back to 0 millimeters per second in 0.125 second. The second curve, which is solid, is for reduced properties with a 60 percent spring factor. This curve decreases from 0 to negative 220,000 millimeters per second in about 0.06 second, then decays rapidly back to negative 40,000 millimeters per second in 0.07 second. Then the curve continues to oscillate and decay gradually back to negative 18,000 millimeters per second in 0.15 second. The third curve, which is long dashes, is for baseline properties with a 60 percent spring factor. This curve decreases from 0 to negative 265,000 millimeters per second in about 0.068 second, then decays rapidly back to 0 millimeters per second in 0.11 second. The fourth curve, which is short dashes, is for reduced properties with a 80 percent spring factor. This curve decreases from 0 to negative 190,000 millimeters per second in about 0.08 second, then decays gradually back to 0 millimeters per second in 0.14 second.

Figure 198. Graph. Good comparison of measured and calculated acceleration histories for the reduced fixed parapet mesh (spring stiffened using 80 percent deflection scale factor). The Y-axis is acceleration in units of millimeters per second. It ranges from negative 220,000 to 0 millimeters per second. The X-axis is time in units of seconds. It ranges from 0 to 0.20 second. Three curves are shown. The first curve, which is dashed, is a calculation for reduced concrete properties with a spring stiffened with an 80 percent displacement factor. This curve decreases from 0 to negative 190,000 millimeters per second in about 0.08 second, then decays gradually back to 0 millimeters per second in 0.14 second. The second curve, which is solid, is a measurement from test P3. This curve decreases from 0 to negative 175,000 millimeters per second in about 0.08 second, then decays gradually, and with oscillations, back to 10,000 millimeters per second in 0.20 second. The third curve, which is dotted, is a measurement for test P4. This curve decreases from 0 to negative 150,000 millimeters per second in about 0.088 second, then decays back to negative 20,0000 millimeters per second in 0.11 second. It continues to decay gradually to about 0 millimeter in 0.20 second. The calculation is in good agreement with the test data.

Figure 199. Graph. Addition of the deck model improves correlations with the test data (spring stiffened using 80 percent deflection scale factor). The Y-axis is acceleration in units of millimeters per second. It ranges from negative 220,000 to 0 millimeters per second. The X-axis is time in units of seconds. It ranges from 0 to 0.20 second. Four curves are shown. Two are calculations, and two are test measurements. Both calculations are for reduced concrete properties with a spring stiffened with an 80 percent displacement factor. The first curve, which is long and short dashed, is a calculation conducted with the deck modeled. This curve decreases from 0 to negative 182,000 millimeters per second in about 0.07 second, then decays gradually, with oscillations, back to 0 millimeters per second in 0.16 second. The second curve, which is dashed, is a calculation conducted without the deck modeled, by fixing the end of the parapet. This curve decreases from 0 to negative 190,000 millimeters per second in about 0.08 second, then decays gradually back to 0 millimeters per second in 0.14 seconds. The third curve, which is solid, is a measurement from test P3. This curve decreases from 0 to negative 175,000 millimeters per second in about 0.08 second, then decays gradually, and with oscillations, back to 10,000 millimeters per second in 0.20 second. The fourth curve, which is dotted, is a measurement for test P4. This curve decreases from 0 to negative 150,000 millimeters per second in about 0.088 second, then decays back to negative 20,0000 millimeters per second in 0.11 second. It continues to decay gradually to about 0 millimeter in 0.20 second. Both calculations are in good agreement with the test data. The calculation with the deck modeled is best, particularly at late time due to the formation of a gradually decaying tail.

Figure 200. Graph. All calculations run with baseline or slightly reduced properties (repow equals 0.5 and G subscript lowercase FS over G subscript lowercase FT equals 0.5) produce rail deflections within two standard deviations of the measured results. The Y-axis is rail deflection in millimeters. It ranges from 0 to 180 millimeters. The X-axis is pendulum spring scale factor in percent. It ranges from 60 to 100 percent. Two main curves are shown. The solid curve is for baseline properties, while the dashed curve is for reduced properties. Each curve is formed from the rail deflection calculated at various spring scale factors, as listed in Table 8. Also shown in this figure are dotted and dashed lines representing the range of deflections that are within one and two standard deviations of the measured results for tests P3 and P4. Deflections lie within one standard deviation of test results if they are between 38 and 125 mm. Deflections lie within two standard deviations of the test results if they are between 0 and 168 mm. The rail deflection curve for baseline properties is within one standard deviation for a 60 to 85 percent scale factor. All of the baseline curve is within two standard deviations of the measured results. The rail deflection curve for reduced properties is within one standard deviation for a 80 to 100 percent scale factor, and is within two standard deviations for a 75 to 80 percent scale factor.

Figure 201. Illustration. Deflection and damage calculated with baseline properties using a stiffened spring (80 percent displacement scale factor). This figure shows two computed views. One is a side view showing the deformed configuration of the bridge rail as it is attached to the concrete parapet. The baseplate is slightly rotated and lifted off the parapet. The honeycomb on the front of the bogie vehicle is crushed about three-fourths of the way. The other is a view looking down on the top of the parapet, with the rail and baseplate removed. It reveals erosion extending into the top of the parapet, and damage fringes extending along the back face.

Figure 202. Illustration. Closeup of damage calculated with baseline properties using a stiffened spring (80 percent displacement scale factor). This is a closeup of the view from Figure 204, looking down on the top of the parapet, with the rail and baseplate removed. It reveals more details of the erosion pattern, such as two rows of erosion on the top face, culminating in an at-angle erosion pattern on each end.

Figure 203. Illustration. Deflection and damage calculated with slightly reduced properties using a stiffened spring (80 percent displacement scale factor). This figure shows two computed views. One is a side view showing the deformed configuration of the bridge rail as it is attached to the concrete parapet. The baseplate is moderately rotated and lifted off the parapet. The honeycomb on the front of the bogie vehicle is crushed about 85 percent. The other is a view looking down on the top of the parapet, with the rail and baseplate removed. It reveals lots of erosion extending into the top of the parapet, and damage fringes with erosion extending along the back face.

Figure 204. Illustration. Closeup of damage calculated with slightly reduced properties using a stiffened
spring (80 percent displacement scale factor). This is a closeup of the view from Figure 206, looking down on the top of the parapet, with the rail and baseplate removed. It reveals more details of the erosion pattern. Rather than in two neat rows, extensive erosions occur about three-fourths of the way through the parapet thickness. It culminates in an at-angle erosion pattern on each end, which extends down the back side of the parapet.

Figure 205. Graph. Larger rail deflections are calculated at 9,835 millimeters per second (large dots) compared with 9,556 millimeters per second (solid and large dashed lines). This figure is the same as Figure 200, except five additional points are plotted, and are represented as large dots. The five additional points are for calculations conducted at 9,835 millimeters per second, as listed in Table 18. The other curves in this figure are for calculations conducted at 9,556 millimeters per second. For a given pendulum spring scale factor, all calculations conducted at 9,835 millimeters per second give larger deflections than those conducted at 9,556 millimeters per second. The Y-axis is rail deflection in millimeters. It ranges from 0 to 180 millimeters. The X-axis is pendulum springs scale factor in percentage. It ranges from 60 to 100 percent. Two main curves are shown. The solid curve is for baseline properties, while the dashed curve is for reduced properties. Each curve is formed from the rail deflection calculated at various spring scale factors, as listed in Table 18. Also shown in this figure are dotted and dashed lines representing the range of deflections that are within one and two standard deviations of the measured results for tests P3 and P4. Deflections lie within one standard deviation of test results if they are between 38 and 125 millimeters. Deflections lie within two standard deviations of the test results if they are between 0 and 168 millimeters. The rail deflection curve for baseline properties is within one standard deviation for a 60 to 85 percent scale factor. All of the baseline curve is within two standard deviations of the measured results. The rail deflection curve for reduced properties is within one standard deviation for a 80 to 100 percent scale factor, and is within two standard deviations for a 75 to 80 percent scale factor.

Figure 206. Illustration. The tensile damage at the base of the parapet is eliminated if a flexible joint is modeled (80 percent displacement scale factor with baseline properties). Two side views of the computed deformed deflection are shown. One calculation used the Contact_Tied_Nodes_To_Surface option. Damage fringes are evident in the parapet at its intersection with the deck. The other calculation used the Contact_Nodes_To_Surface option. Damage fringes are no longer evident in the parapet at its intersection with the deck.